Related papers: Random graphs with arbitrary degree distributions …
Consider a random bipartite multigraph $G$ with $n$ left nodes and $m \geq n \geq 2$ right nodes. Each left node $x$ has $d_x \geq 1$ random right neighbors. The average left degree $\Delta$ is fixed, $\Delta \geq 2$. We ask whether for the…
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
In this paper we study the behavior of maximum out/in-degree of binomial/Poisson random scaled sector graphs in the presence of random vertex and edge faults. We prove that the probability distribution of maximum degrees for random faulty…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph.…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
We establish the asymptotic degree distribution of the typical vertex of inhomogeneous and passive random intersection graphs under the minimal moment conditions.
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…
Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
We delve into the statistical properties of regions within complex networks that are distant from vertices with high centralities, such as hubs or highly connected clusters. These remote regions play a pivotal role in shaping the asymptotic…